I should note that I eventually intend to take both Prob & Stats and Abstract Algebra, so it's not really that important which one I take now. But in any case, here is when the classes are available this fall (TR = Tuesday/Thursday, MW = Monday/Wednesday):

Principles of Programming LanguagesTR 1:00-300

Prob & StatsTR 11:00-1:00MW 7:00-9:00 (PM)

Linear AlgebraTR 1:00-3:00MW 5:00-7:00 (PM)

Abstract AlgebraTR 7:00-8:15 (PM)

I try really hard to avoid taking classes during the day. I also try, though much less hard, to get Tuesday/Thursday classes rather than Monday/Wednesday ones.

It's pretty clear that the obvious choice of two classes from this list is Linear Algebra and Prob & Stats on Monday and Wednesday nights. That puts them in a solid block from 5-9, which is similar to the schedule I started this semester with (though I have Tuesday/Thursdays instead).

My fear is that the same professor will be teaching linear algebra again. I really don't want to take it from him. It's still "TBA" right now. But if he teaches it at night two semesters in a row, then there's no reason to think he won't do it next Spring too, so there's kind of no point in skipping it for that reason.

This is a lot of hours. It's possible I could instead take Prob & Stats and Abstract Algebra. I'd have class four nights a week, and having a single class at 7PM two days a week is not that great, but I could use the time before class to do homework. And it would be 7 rather than 8 credit hours.

But linear algebra, unlike either of the other two maths, is non-negotiable, so leaving it for Spring of '09 would mean I'd have to take it at that point. As things stand now, the only class I'll actually have to take next Spring is Principles of Programming Languages.

I guess we'll see next semester if I can really get through those two courses. At least the first half or so of linear should be easy the second time through.

Linear algebra is simply consuming all of my available time. It doesn't help that I have a terrible professor. (It helps that Ed loves it, and helps me with it a lot. But this doesn't save me time, really - it just gives me a better understanding of the material. And something fun to do.) It really doesn't help that linear algebra homework is so much more straightforward than working on my sweprac project, and so much more deadline-driven, that at any given moment I am bound to choose it.

But sweprac is important. It's my senior experience course. It's only taught in the Spring. I really, truly do not want to have to re-take it. I also don't want to let down my professor - who is happy for me to finally have the positive group experience I've never had. And I really do have a fantastic team for the class. I owe them my effort, and it's also a great opportunity to really do something.

The idea of re-taking linear algebra another time sounds perfectly fun and delightful, so it's not a loss in that way. Maybe I'll even get a good professor next time.

Wednesday, March 12, 2008

My current resolution is to turn screens (computer and TV, though the latter isn't much of a problem for me) off at 10 PM. Ed's under strict instructions not to talk to me via IM after that time. And, if I'm at my house, I've asked him to kick me out by 9:30. (It's a 10-minute drive back to my place.)

I have eight (8) sections of homework due next Thursday. I got a week behind, and next Thursday is the test, so it would be good to be caught up, though probably not all eight of those sections will be on the test. But our professor hasn't said which ones will, and I don't intend to go back to class again until the test itself, so I had better just finish all of them.

I've done one section, so basically, if I complete one per day from here on out, I'll be fine. But there's really no such thing as completing one section per day. While I can't exactly sit down and do several sections in a row, I also can't usually complete a whole section on the first pass. So I need to do some unspecified amount of work that averages, by Thursday, to a section a day.

This is the most boring blog post ever.

Anyway, aside from this trauma, things are all right. At some point I will need to do some work for sweprac if I'm to pass that. The week after next is Spring Break. I might survive.

Sunday, March 09, 2008

OK, so, it's not all that fabulous, but think about this. In our sky you can see lots of stars in our galaxy. Our galaxy is huge. And then, also in our sky, you can see whole other galaxies. They are so far away that they are, like, the same apparent size as stars.

It is just freakin' amazing the range of orders of magnitude present in our universe. It reminds me of this, of course (from Monty Python's The Meaning of Life, which I remember seeing in the theater in New Orleans as a little kid, with my mom and her friend and her friend's kids):

The other day, I showed up at Ed's house, found the front door unlocked, raced up the stairs to his room, met him in the hall, and said, "Your girlfriend is a fucking brilliant math genius!"

Let's back it up.

I'm not a math genius. I am pretty good at math, and getting better all the time. I also think that almost anyone can learn and enjoy math, and that most people who think they are "bad at math" just haven't had good experiences with it and thus haven't stuck to it. (This applies double to my mom, who loves formal logic and puzzles and therefore is obviously math-inclined despite apparently never having enjoyed math itself.)

But math can really kick you around. Unlike history or literature, where you have progressively increased knowledge leading to mastery and insights, math can make you feel really stupid when you don't get it. (I might not understand the causes of the Great Depression, but this makes me feel, at worst, ignorant. When I do know some history, I am unaware of my lack of insight about it. You don't have to have the proper insights to understand what others have written.) The flip side of feeling like an idiot when you don't understand math, though, is feeling like a genius when you do.

Last week, I had a section on transition matrices and change of basis. (I promise I won't talk about this in detail.) I did all of the homework pretty quickly by stumbling (by some insight I couldn't recreate until recently) onto a method that worked, but when I triumphantly showed it to Ed, he didn't like my method (he's not a fan of the augmented matrix; he prefers an algebraic approach).

When we sat down to figure out the actual algebra, we found the section of the book rather inscrutable. (I have since seen the completely clear presentation in his linear algebra book, so I have a basis for comparison. No pun intended.) What we found by deduction from what I'd done in my homework didn't seem to make any sense, and Ed didn't feel it was consistent with the book's text. He hypothesised (hypothesied? hypothesized?) that someone different had written the questions from whoever wrote the text, and that the two didn't match. He also found that the questions and answers were not themselves consistent.

"But I did them all the same way," I protested, "based on what I read. And my answers match the ones in the back."

I said this over and over, but I couldn't show how it was true, because I had lost the understanding of what I'd done, somehow. I'd lost the knowledge of how it made sense.

I don't want to make it sound like I just rolled over, either. We worked on this hard for a long time, on two different days. We came to a conclusion about how most of the problems worked, but the conclusion was just stupid. It would sometimes require things to be multiplied backwards, in the direction that doesn't work for matrices. And it was just plain not sensible, even though it was workable in a lot of instances.

I was troubled. The night before my breakthrough, I felt that I thought about these problems all night while I slept. By morning, I had a new tack to try, and I hastened to the library to work it out.

By 90 or so minutes later, I was ready. I had figured out how to show that the book was consistent, correct, and sensible, and I was eager to demonstrate this to Ed. We had been stupid and missed a kind of obvious point. (For my fellow linear algebra students, I will state the central insight thusly: a transition matrix does not change a basis to another basis; it changes a vector stated in terms of one basis to the same vector in terms of a different basis.)

Hence my rushing up the stairs, declaration of myself as a genius, etc.

Ed was skeptical. We'd worked pretty hard and pretty clearly on this, after all.

"We're going to run this like a game," I said. "And games have rules, right?"

"Does this mean our relationship is a game?" he asked.

"Yes, but you knew that already."

"I guess you're right."

"OK," I said. "These are the rules. You can't go ahead of me, and you can't go sideways from me. You have to let me show you this. You can only interrupt me if you think I've done something wrong, or if you don't understand what I'm doing."

"No going forward, no going sideways. But I can go backwards? Got it."

We chatted a little more while he made some tea. He asked if I was going to be crushed if he didn't agree with me, once I had showed him my argument. I told him I'd only be crushed if I still thought I was right, but that I was confident we could come to an agreement either way. He was pretty sure I was going to turn out to be wrong.

I wasn't. In fact, once I gave him the central insight, the rest pretty much fell into place, though I went through my demo anyway. It was terrifically fun. Some of my algebra was wrong (for instance, in one place I divided each side of an equation by a vector, which is an undefined operation), but it led to the place we'd ended up the other day anyway, except that now that place didn't seem nonsensical. (The algebra worked in the other direction, just not in the way I'd derived it. What I provided was not in any way a proof, but I did show some relationship between our work the other day and the sensical way that the book was really working.)